# Can you please explain what formula I need to do to solve the following problem:

If 3 laps = 5/8 mile, how many laps needs to be completed to run 3 miles?

Don't look for "formulas" to do these kind of questions, use ratios, one of the most powerful tools of math

3 laps = 5/8 mile

x laps = 3 miles

so

3/x = (5/8)/3

cross-multiply

(5/8)x = 9

x = 9(8/5)

=14.4 laps

## To solve this problem, you can use ratios.

First, you know that 3 laps is equal to 5/8 mile.

To find out how many laps are needed to run 3 miles, you need to set up a proportion.

Let x represent the number of laps needed to run 3 miles.

You can set up the proportion as follows:

3 laps / x laps = 5/8 mile / 3 miles

To solve for x, you cross-multiply:

3 miles * 5/8 mile = x laps * 1

15/8 miles = x laps

To isolate x, you multiply both sides by the reciprocal of 15/8:

8/15 * 15/8 miles = x laps * 8/15

1 mile = x laps * 8/15

Now, divide both sides by 8/15 to solve for x:

1 mile / (8/15) = x laps

Multiply 1 mile by the reciprocal of 8/15:

1 mile * 15/8 = x laps * (15/8)

15/8 miles = x laps

Therefore, x is equal to 15/8 laps, which is equivalent to 1.875 laps.

So, you would need to complete approximately 1.875 laps to run 3 miles.

## To solve the problem, we can use a ratio to find the number of laps needed to run 3 miles.

First, we are given that 3 laps is equal to 5/8 mile.

Next, we want to find the number of laps needed to run 3 miles, which we'll call x laps.

We can set up a proportion using the ratios of laps to distance:

3 laps / (5/8) mile = x laps / 3 miles

To solve the proportion, we cross-multiply:

(5/8)x = 9

To isolate x, we divide both sides of the equation by 5/8:

x = 9 / (5/8)

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/8 is 8/5, so we multiply both sides of the equation by 8/5:

x = 9 * (8/5)

Multiplying the numerators and denominators gives us:

x = 72/5

Therefore, the number of laps needed to run 3 miles is 72/5 laps, which simplifies to 14.4 laps.